Seven-dimensional Einstein Manifolds from Tod-Hitchin Geometry

Makoto Sakaguchi; Yukinori Yasui

doi:10.1016/j.geomphys.2006.01.003

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arXiv · hep-th/0411165

Seven-dimensional Einstein Manifolds from Tod-Hitchin Geometry

Makoto Sakaguchi·Yukinori Yasui

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Abstract

We construct infinitely many seven-dimensional Einstein metrics of weak holonomy G_2. These metrics are defined on principal SO(3) bundles over four-dimensional Bianchi IX orbifolds with the Tod-Hitchin metrics. The Tod-Hitchin metric has an orbifold singularity parameterized by an integer, and is shown to be similar near the singularity to the Taub-NUT de Sitter metric with a special charge. We show, however, that the seven-dimensional metrics on the total space are actually smooth. The geodesics on the weak G_2 manifolds are discussed. It is shown that the geodesic equation is equivalent to the Hamiltonian equation of an interacting rigid body system. We also discuss M-theory on the product space of AdS_4 and the seven-dimensional manifolds, and the dual gauge theories in three-dimensions.

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BibTeX RIS

Makoto Sakaguchi, Yukinori Yasui. 2004-12-10. Seven-dimensional Einstein Manifolds from Tod-Hitchin Geometry. https://doi.org/10.1016/j.geomphys.2006.01.003

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